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Three bottles of equal capacity containing mixture of milk and water in ratio 2 : 5, 3 : 4 and 4 : 5 respectively. These three bottles are emptied into a large bottle. What will be the ratio of milk and water respectively in the large bottle?1). 73 : 1062). 73 : 1163). 73 : 1134). 73 : 189 |
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Answer» Let the capacity be Z litres For bottle 1, 2 : 5 implies that milk is 2a and water is 5a ⇒ 2a + 5a = z ⇒ a = z/7…..(i) For bottle 2, 3 : 4 implies that milk is 3b and water is 4B ⇒ 3b + 4b = z ⇒ b = z/7…..(ii) For bottle 1, 4 : 5 implies that milk is 4c and water is 5c ⇒ 4c + 5c = z ⇒ c = z/9…..(III) Total milk is = 2a + 3b + 4c Using (i), (ii) and (iii) ⇒ milk = 2 × z/7 + 3 × z/7 + 4 × z/9 Total water is 5a + 4b + 5c ⇒ water = 5 × z/7 + 4 × z/7 + 5 × z/9 Ratio of milk and water is GIVEN as ⇒ (2 × z/7 + 3 × z/7 + 4 × z/9) / ( 5 × z/7 + 4 × z/7 + 5 × z/9) ⇒ 73/116 ∴ ratio is 73 : 116 |
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